Robust Point Set Registration Using Signature Quadratic Form Distance

Point set registration is a problem with a long history in many pattern recognition tasks. This paper presents a robust point set registration algorithm based on optimizing the distance between two probability distributions. A major problem in point to point algorithms is defining the correspondence between two point sets. This paper follows the idea of some probability-based point set registration methods by representing the point sets as Gaussian mixture models (GMMs). By optimizing the distance between the two GMMs, rigid transformations (rotation and translation) between two point sets can be obtained without having to find a correspondence. Previous studies have used L2, Kullback Leibler, etc. distance to measure similarity between two GMMs; however, these methods have problems with robustness to noise and outliers, especially when the covariance matrix is large, or a local minimum exists. Therefore, in this paper, the signature quadratic form distance is derived to measure the distribution similarity. The contribution of this paper lies in adopting the signature quadratic form distance for the point set registration algorithm. The experimental results show the precision and robustness of this algorithm and demonstrate that it outperforms other state-of-the-art point set registration algorithms regarding factors, such as noise, outliers, missing partial structures, and initial misalignment.